$$14x\cdot4+28x\cdot3-7x\cdot\dfrac{2}{7}x=\dfrac{-14x^2+980x}{7}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}14x\cdot4+28x\cdot3-7x\cdot\frac{2}{7}x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}56x+84x-7x\cdot\frac{2}{7}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}140x-7x\cdot\frac{2}{7}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(140-7x\cdot\frac{2}{7})x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(140-\frac{14x}{7})x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{-14x+980}{7}x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{-14x^2+980x}{7}\end{aligned} $$ | |
| ① | $$ 14 x \cdot 4 = 56 x $$ |
| ② | $$ 28 x \cdot 3 = 84 x $$ |
| ③ | Combine like terms: $$ \color{blue}{56x} + \color{blue}{84x} = \color{blue}{140x} $$ |
| ④ | Use the distributive property. |
| ⑤ | Multiply $7x$ by $ \dfrac{2}{7} $ to get $ \dfrac{ 14x }{ 7 } $. Step 1: Write $ 7x $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 7x \cdot \frac{2}{7} & \xlongequal{\text{Step 1}} \frac{7x}{\color{red}{1}} \cdot \frac{2}{7} \xlongequal{\text{Step 2}} \frac{ 7x \cdot 2 }{ 1 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 14x }{ 7 } \end{aligned} $$ |
| ⑥ | Subtract $ \dfrac{14x}{7} $ from $ 140 $ to get $ \dfrac{ \color{purple}{ -14x+980 } }{ 7 }$. Step 1: Write $ 140 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |
| ⑦ | Multiply $ \dfrac{-14x+980}{7} $ by $ x $ to get $ \dfrac{ -14x^2+980x }{ 7 } $. Step 1: Write $ x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{-14x+980}{7} \cdot x & \xlongequal{\text{Step 1}} \frac{-14x+980}{7} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( -14x+980 \right) \cdot x }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -14x^2+980x }{ 7 } \end{aligned} $$ |